Newton's third law
Particles exert equal and opposite forces on one another: if is the force on the -th particle due to the -th particle, then .
Internal forces cancel in pairs
In a system of particles, the force on the -th particle splits as
and the third law makes the internal contributions cancel in pairs:
Hence , so the total momentum of a system is conserved in the absence of external forces. When internal forces are derived from pair potentials , the third law also requires .
Rocket thrust
Consider a rocket that ejects fuel with speed relative to the rocket, moving in a straight line. The process of ejection can be complicated, but the total momentum must obey , so comparing momenta at times and gives
called the Tsiolkovsky rocket equation. Equivalently,
where is the thrust force exerted on the rocket by the ejected fuel.
Related
Stated in
- Law 4.1 (Newton's Third Law)§4 Systems of Particles